Finding the addition rules

Using the number line to solve addition problems will always work. However, it might be considered a little childish if you are still using a number line to answer questions while in high school! In this lesson you will find two rules to make adding negative numbers (especially ones with large absolute values) easier. Consider the following problems. Solve them with a number line and then look for patterns that will allow you to solve the problems without the number line.

Add each of the following problems.

1. -6 + (-3) =

9. 8 + (-5) =

2. -9 + (-2) =

10. 9 + (-7) =

3. -5 + (-3) =

11. -9 + 4 =

4. (+8) + (+5) =

12. 3 + (-1) =

5. -7 + (-7) =

13. -7 + 9 =

6. (+3) + (+6) =

14. 2 + (-11) =

7. -4 + (-4) =

15. -13 + 5 =

8. All of the problems in the above column involved adding numbers with the same sign. Write a rule that makes adding the same signs easy to do.

16. All of the problems in the above column involved adding numbers with different signs. Write a rule that makes adding numbers with different signs easy to do.

Let's find the rules by looking at the following four problems.

Adding the same signs

Adding different signs

(+5) + (+3) = +8

(+5) + (-2) = +3

(-10) + (-5) = -15

(-6) + (+10) = +4

In these examples we can find two rules for making addition simpler:

When adding two numbers with the same sign:
Add the absolute values of the numbers and attach the sign of the numbers to the sum.

When adding two numbers with different signs:
Subtract the absolute values of the two numbers and attach the sign of the number with the largest absolute